Method of decoding LDPC code for producing several different decoders using parity-check matrix of LDPC code and LDPC code system including the same

ABSTRACT

Provided are a method of decoding an LDPC code for producing several different decoders using a parity-check matrix of the LDPC code, and an LDPC code system including the same. The system includes: an LDPC encoder outputting an LDPC codeword through a channel; a first LDPC decoder decoding the LDPC codeword received through the channel, and when the decoding has failed in a second LDPC decoder, decoding the LDPC codeword according to original parity check matrix of the LDPC codeword, using soft information newly generated after the decoding is ended in the second LDPC decoder; and the second LDPC decoder, when the decoding has failed in the first LDPC decoder, receiving the soft information on each bit from the first LDPC, and decoding the LDPC codeword according to a new parity-check matrix produced from the parity-check matrix of the LDPC codeword using the received soft information on each bit.

CROSS-REFERENCE TO RELATED APPLICATIONS AND CLAIM OF PRIORITY

This application claims priority from and the benefit of Korean PatentApplication No. 10-2011-0145651, filed on Dec. 29, 2011, and KoreanPatent Application No. 10-2012-0041105, filed on Apr. 19, 2012, thedisclosures of which are incorporated herein by reference.

BACKGROUND

1. Technical Field

The present disclosure relates to a method of decoding a low-densityparity-check (LDPC) code and an LDPC code system using the same.

2. Description of Related Art

An LDPC code is a linear block code and includes k-bit information andp-bit parity. That is, the total length n is the sum of k and p. A coderate representing the ratio of an information bit in length to the totallength may be represented by the expression k/n. During encoding of theLDPC code, using a parity-check matrix, an input of k is received and anoutput of n is output.

A decoding algorithm of the LDPC code is based on a message passingalgorithm. The message passing algorithm mainly includes two processes.First, bit-to-check message passing is performed. During bit-to-checkmessage passing, bit nodes bound to the same check node transceivemessages with each other in order to provide information on other bitnodes in the same group. Here, the bit-to-check bound structure is fixedso that the sum of bit determination values bound to the common checkaccording to the parity-check matrix becomes an even number (to satisfyan even parity condition). After the bit-to-check message passingprocess, check-to-bit message passing is performed. During thecheck-to-bit message passing, check nodes bound to a single bit nodeperform an operation of transceiving messages with each other. Thebit-to-check message passing and the check-to-bit message passing areiteratively performed until the LDPC code is decoded into a validcodeword or until the maximum iteration count has reached. When the LDPCcode is used in connection to other codes, error correction ability isenhanced. However, parity bits are increased due to an additionalencoding process, there is a problem in that code rate is reduced. Inaddition, an additional encoding process, and an increase in complexitydue to a corresponding additional decoding process may not be avoided.

A basic LDPC code system according to related art may include, asillustrated in FIG. 1, an LDPC encoder that encodes an LDPC code whichis input data so as transmitted to a channel, and an LDPC decoder thatreceives and decodes the LDPC code received through the channel.

A decoding process of the LDPC decoder is iteratively performed until adetermined value (x_hat) becomes a valid codeword, or until the maximumiteration count has reached.

However, the LDPC code system having the above configuration accordingto the related art has problems in that, as described above, since theLDPC code is used in connection to other codes for the error correctionability, parity bits are increased due to an additional encoding processand thus code rate is reduced. In addition, there are problems of anadditional encoding process and an increase in complexity due to acorresponding additional decoding process.

SUMMARY

According to an aspect of the present invention, the present disclosureis directed to providing a method of decoding an LDPC code and a LDPCcode system including the same, capable of producing several differentdecoders using a single LDPC parity-check matrix.

According to an aspect of the present invention, the present disclosureis also directed to providing a method of decoding an LDPC code and aLDPC code system including the same, in which an additional encodingprocess is not needed, an existing code is used as it is, and thus coderate is not changed.

According to an aspect of the present invention, the present disclosureis also directed to providing a method of decoding an LDPC code and aLDPC code system including the same, in which a second LDPC decoder isoperated only when a first LDPC decoder has failed in error correction,and thus speed loss due to an additional operation may be minimized.

The technical problems of the disclosure are not limited to thosementioned above, and other problems that are not mentioned may beclearly understood by those skilled in the art from the descriptionbelow.

In one general aspect, the present disclosure provides a method ofdecoding an LDPC code including: (a) outputting an LDPC codeword from anLDPC encoder through a channel; (b) decoding the LDPC codeword outputthrough the channel by a first LDPC decoder; (c) when the decoding hasfailed in the first LDPC decoder, receiving soft information on each bitfrom the first LDPC and decoding the LDPC codeword according to a newparity-check matrix produced from a parity-check matrix of the LDPCcodeword, by a second LDPC decoder; (d) when the decoding has failed inthe second LDPC decoder, receiving soft information newly generatedafter the decoding is ended from the second LDPC decoder and decodingthe LDPC codeword according to the parity-check matrix of the LDPCcodeword, by the first LDPC decoder; and (e) iteratively performing (c)and (d) until the LDPC code is decoded or until a maximum iterationcount.

In another general aspect, the present disclosure provides an LDPC codesystem including: an LDPC encoder outputting an LDPC codeword through achannel; a first LDPC decoder decoding the LDPC codeword receivedthrough the channel, and when the decoding has failed in a second LDPCdecoder, decoding the LDPC codeword according to a parity-check matrixof the LDPC codeword, using soft information newly generated after thedecoding is ended in the second LDPC decoder; and the second LDPCdecoder, when the decoding has failed in the first LDPC decoder,receiving the soft information on each bit from the first LDPC, anddecoding the LDPC codeword according to a new parity-check matrixproduced from the parity-check matrix of the LDPC codeword using thereceived soft information on each bit.

Here, the new parity-check matrix may have new rows produced by linearoperations on rows in the parity-check matrix of the LDPC codeword.

In addition, the new parity-check matrix may have new columns producedby linear operations on columns in the parity-check matrix of the LDPCcodeword.

In addition, the new parity-check matrix may have new rows and columnsproduced by linear operations on rows and columns in the parity-checkmatrix of the LDPC codeword.

When the even or odd number of rows or columns are combined through thebinary addition, bit nodes bound to two check nodes may be bound to acombined check node, and an overlapping bit node may be broken. Inaddition, the soft information may be probability information of “1” or“0” on each bit.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of a basic LDPC code system according torelated art.

FIG. 2 is a block diagram of an LDPC code system according to anexemplary embodiment of the disclosure.

FIG. 3 is a diagram illustrating an example of generating a row of a newparity-check matrix by combining two rows of a parity-check matrixthrough binary addition.

FIG. 4 is a diagram illustrating an example of combining two check nodesinto a single check node.

FIG. 5 is a graph showing the results of a simulation of errorcorrection abilities according to signal-to-noise ratio (SNR) of theLDPC code system according to the related art and the LDPC code systemproposed by the disclosure.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Exemplary embodiments now will be described more fully hereinafter withreference to the accompanying drawings, in which exemplary embodimentsare shown. The present disclosure may, however, be embodied in manydifferent forms and should not be construed as limited to the exemplaryembodiments set forth therein. In addition, in the drawings, parts thatare not related to the description may be omitted to clearly describethe disclosure, and like elements are denoted by like reference numeralsthrough the specification.

Hereinafter, specific technical contents of the disclosure are describedin detail with reference to the accompanying drawings.

FIG. 2 is a block diagram of an LDPC code system according to anexemplary embodiment of the disclosure.

The LDPC code system of the disclosure includes, as illustrated in FIG.2, an LDPC encoder 110, a channel 120, a first LDPC decoder 130, and asecond LDPC decoder 140.

The LDPC encoder 110 encodes an LDPC code which is input data so as tobe transmitted to the channel 120.

In the LDPC encoder 110, in order to transmit the data to be transmittedto the channel 120 without loss and deterioration, an LDPC codingprocedure is performed. The data subjected to the channel codingprocedure may be transmitted as a single symbol by collecting severalbits when the data is transmitted to the wireless channel 120. Here, aprocedure of mapping several bits into a symbol is referred to asmodulation.

The modulated data is converted into a signal for multiple transfersthrough a multiplexing process or a multiple access method. As themultiplexing method, there are various methods including CDM, TDM, andFMD. The signal passing through the multiplexing block is changed to astructure appropriate for being transmitted to one or more multipleantennas and is transmitted to a receiver through the wireless channel.The data transmitted in this process undergoes fading, column noise, andthe like, so that deterioration of data may occur. The receiving endreceives the deteriorated data and then performs a series of proceduresof the transmitting end in the reverse order. A modulation operation ofchanging the data mapped into the symbol to a bit string is performed,and the data deteriorated through the channel decoding procedure isrestored to the original data.

The LDPC encoder 110 that performs the channel coding stores an H matrixwhich is a parity-check matrix used for generating parity bits to beadded to the input data (information bits or systematic bits), or ageneration matrix G derived from the H matrix. That is, the LDPC encodergenerates parity bits from the H or G matrix and the input data.

The first and second LDPC decoders 130 and 140 are devices forperforming channel decoding, confirm whether or not the data (systematicbits) input through the operation of the received data (deterioratedsystematic bits+parity bits) and the H matrix is reliably restored, andperform the operation again when the recovery has failed.

Specifically, the first LDPC decoder 130 decodes an LDPC codewordreceived through the channel 120. Here, in the first LDPC decoder 130,when decoding has failed, the second LDPC decoder 140 receives softinformation on each bit from the first LDPC 130, and decodes an LDPCcodeword according to a new parity-check matrix generated from theparity-check matrix of the LDPC codeword using the received softinformation on each bit. Here, the soft information representsprobability information of “1” or “0” on each bit. That is, according tothe disclosure, the same auxiliary LDPC decoder as the second LDPCdecoder that performs decoding according to a new parity-check matrixproduced from the parity-check matrix of the first LDPC decoder is used.The auxiliary LDPC decoder may be changed in number. In addition, thefirst LDPC decoder and the auxiliary LDPC decoders may constitute aserial concatenation, a parallel concatenation, or a combination ofserial and parallel concatenations.

If decoding has failed even in the second LDPC decoder 140, the firstLDPC decoder 130 decodes the LDPC codeword according to the newparity-check matrix generated from the parity-check matrix of the LDPCcodeword, using soft information newly generated after the decodingoperation of the second LDPC decoder 140 is ended.

In this manner, in the embodiment of the disclosure, until the LDPC codeis decoded or until the maximum iteration count, the LDPC codeword isdecoded through a feedback process in which extrinsic information istransceived between the first and second LDPC decoders 130 and 140.

Here, the new parity-check matrix may have new rows or columns generatedby linear operations on rows or columns in the parity-check matrix ofthe LDPC codeword, or have new rows and columns generated by linearoperations on rows and columns in the parity-check matrix of the LDPCcodeword. The new parity-check matrix will be described in detail withreference to FIGS. 3 and 4 described later.

The second LDPC decoder 140 is produced on the basis of the parity-checkmatrix newly generated by the method proposed by the disclosure. TheLDPC code system of the disclosure has an advantage that, since anadditional encoding process is absent, complexity of the transmissionside is maintained and code rate is not changed. In addition, duringdecoding by the reception side, the second LDPC decoder 140 is designedto operate only when the first LDPC decoder 130 has failed in decoding,so that speed loss due to the additional operation may be minimized.That is, when the first LDPC decoder 130 has failed in decoding on thereception side, the second LDPC decoder 140 receives the softinformation on each bit from the first LDPC decoder 130 so as tooperate. Here, after the operation of the second LDPC decoder 140 isended, the newly generated soft information is transmitted to the firstLDPC decoder 130. That is, the first and second decoders 130 and 140undergo the feedback process in which extrinsic information istransceived.

Next, a method of designing the second LDPC decoder 140 will bedescribed. Since the decoder structure of the LDPC code is based on theparity-check matrix, in order to design an additional decoder, anadditional parity-check matrix is needed. An additional parity-checkmatrix proposed by the disclosure is to produce a new row or column, orrow and column from a combination of an even or odd number of rows orcolumns, or rows and columns of a basic parity-check matrix.

FIG. 3 is a diagram illustrating an example of generating a row of a newparity-check matrix by combining two rows of a parity-check matrixthrough binary addition.

As in FIG. 3, a new parity-check matrix is produced by adding two rowsthrough binary addition. Since a change in check node degree (the numberof bit nodes bound to a single check node) due to two binary additionsis even number as it is, an even number parity condition is satisfied asit is. That is, an existing code may be decoded using the newly producedparity-check matrix. Here, decoding can be made using a newly producedmatrix as long as the condition in which the number of combined rows isan even number is satisfied, so that the number of rows does not have tobe 2 (a number of combinations can be made).

In this manner, a new parity-check matrix may be produced by adding aneven or odd number of columns through binary addition, or a newparity-check matrix may be produced by adding an even or odd number ofrows and columns through binary addition.

Meanwhile, an arbitrary parity-check matrix may be represented as abipartite graph configured of check nodes and variable nodes. FIG. 4illustrates an example of combining two check nodes into a single checknode using a bipartite graph.

In FIG. 4, combining two rows means combining two check nodes in thebipartite graph. Here, bit nodes bound to the two check nodes are boundto the combined check node, and an overlapping bit node is broken(characteristics of the boundary addition).

FIG. 5 shows the results of a simulation of error correction abilitiesaccording to signal-to-noise ratio (SNR) of the general LDPC code system(normal) and the LDPC code system proposed by the disclosure. The sameAWGN data was generated at each SNR. Here, I_(D1) and I_(D2)respectively represent the maximum iteration counts of the first LDPCdecoder 130 and the second LDPC decoder 140. I_(G) represents feedbackcounts of the two decoders. That is, the general LDPC code system(normal) in FIG. 5 is a system in which only the first LDPC decoder 130is operated and the maximum iteration count is fixed to 250. On theother hand, in the LDPC code system proposed by the disclosure, thefirst and the second LDPC decoders 130 and 140 have maximum iterationcounts of 40 and 10, respectively, and have a maximum feedback count of5. Consequently, the two systems are both fixed to the 250 maximumiteration counts. According to the simulation results, it can be seenthat the proposed system shows better error correction ability than theexisting system in high SNR areas.

According to one or more embodiments, several different decoders may beproduced using a single LDPC parity-check matrix.

According to one or more embodiments, additional encoding process is notneeded, an existing code is used as it is, and thus code rate is notchanged.

According to one or more embodiments, the second LDPC decoder may beoperated only when the first LDPC decoder has failed in errorcorrection, and thus speed loss due to an additional operation may beminimized.

According to one or more embodiments, as a result of implementing theLDPC code system according to the disclosure, it could be seen thaterror correction ability stronger than that of the LDPC code systemaccording to the related art is shown in a high SNR region.

The advantageous effects of the disclosure are not limited to thosementioned above, and other effects that are not mentioned may be clearlyunderstood by those skilled in the art from the description below.

The exemplary embodiments of the disclosure described above aredisclosed to solve the technical problems. It should be understood bythose skilled in the art that various modifications, alterations, andadditions may occur without departing from the spirit and scope of thedisclosure, and such modifications and alternations are within the scopeof the following claims.

What is claimed is:
 1. A method of decoding a low-density parity-check(LDPC) code, comprising: (a) outputting an LDPC codeword from an LDPCencoder through a channel; (b) decoding the LDPC codeword output throughthe channel by a first LDPC decoder according to a parity check matrixderived from a parity-check matrix of the LDPC codeword; (c) when thedecoding has failed in the first LDPC decoder, receiving softinformation on each bit from the first LDPC decoder and decoding theLDPC codeword according to a new parity-check matrix produced from theparity-check matrix of the LDPC codeword by a second LDPC decoder; (d)when the decoding has failed in the second LDPC decoder, receiving softinformation newly generated after the decoding is ended from the secondLDPC decoder and decoding the LDPC codeword according to said newparity-check matrix used by the first LDPC decoder; and (e) iterativelyperforming (c) and (d) until the LDPC code is decoded or until a maximumiteration count.
 2. The method according to claim 1, wherein the numberof the second LPDC decoder can be changed; the second LDPC decoders aredecoded according to the new parity-check matrix produced from theparity-check matrix of the first LDPC decoder, and the first LDPCdecoder and the second LDPC decoders constitute a decoding system in aserial concatenation, a parallel concatenation, or a combination ofserial and parallel concatenations.
 3. The method according to claim 1,wherein the new parity-check matrix has new rows produced by linearoperations on rows in the parity-check matrix of the LDPC codeword. 4.The method according to claim 3, wherein, when even or odd numbers ofrows or columns are linearly combined through a binary addition, bitnodes bound to two check nodes are bound to a combined check node, andan overlapping bit node is broken.
 5. The method according to claim 1,wherein the new parity-check matrix has new columns produced by linearoperations on columns in the parity-check matrix of the LDPC codeword.6. The method according to claim 5, wherein, when even or odd numbers ofrows or columns are linearly combined through a binary addition, bitnodes bound to two check nodes are bound to a combined check node, andan overlapping bit node is broken.
 7. The method according to claim 1,wherein the new parity-check matrix has new rows and new columnsproduced by linear operations on rows and columns in the parity-checkmatrix of the LDPC codeword.
 8. The method according to claim 7,wherein, when even or odd numbers of rows or columns are linearlycombined through a binary addition, bit nodes bound to two check nodesare bound to a combined check node, and an overlapping bit node isbroken.
 9. The method according to claim 1, wherein the new parity-checkmatrix is derived from a different number of rows and columns from thatof the parity-check matrix of the LDPC codeword.
 10. The methodaccording to claim 1, wherein the soft information is probabilityinformation of “1” or “0” on each bit.
 11. A low-density parity-check(LDPC) code system, comprising: an LDPC encoder outputting an LDPCcodeword through a channel; a first LDPC decoder decoding the LDPCcodeword received through the channel, and when the decoding has failedin a second LDPC decoder, decoding the LDPC codeword according to a newparity-check matrix produced from the parity-check matrix of the LDPCcodeword, using soft information newly generated after the decoding isended in the second LDPC decoder; and the second LDPC decoder, when thedecoding has failed in the first LDPC decoder, receiving the softinformation on each bit from the first LDPC, and decoding the LDPCcodeword according to said new parity-check matrix produced from theparity-check matrix of the LDPC codeword using the received softinformation on each bit.
 12. The system according to claim 11, whereinthe number of the second LDPC decoder can be changed; the second LDPCdecoders are decoded according to the new parity-check matrix producedfrom the parity-check matrix of the first LDPC decoder; and the firstLDPC decoder and the second LDPC decoders constitute a decoding systemin a serial concatenation, a parallel concatenation, or a combination ofserial and parallel concatenations.
 13. The system according to claim11, wherein the new parity-check matrix has new rows produced by linearoperations on rows in the parity-check matrix of the LDPC codeword. 14.The system according to claim 11, wherein the new parity-check matrixhas new columns produced by linear operations on columns in theparity-check matrix of the LDPC codeword.
 15. The system according toclaim 11, wherein the new parity-check matrix has new rows and newcolumns produced by linear operations on rows and columns in theparity-check matrix of the LDPC codeword.